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Research Papers

Identification and Comparison for Continuous Motion Characteristics of Three Two-Degree-of-Freedom Pointing Mechanisms

[+] Author and Article Information
Jingjun Yu

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: jjyu@buaa.edu.cn

Zhao Jin

Robotics Institute,
Beihang University,
Beijing 100191, China

Xianwen Kong

School of Engineering and Physical Sciences,
Heriot-Watt University,
Edinburgh EH14 4AS, UK

Manuscript received February 15, 2017; final manuscript received July 5, 2017; published online August 31, 2017. Assoc. Editor: Marc Gouttefarde.

J. Mechanisms Robotics 9(5), 051015 (Aug 31, 2017) (13 pages) Paper No: JMR-17-1042; doi: 10.1115/1.4037568 History: Received February 15, 2017; Revised July 05, 2017

Two-degree-of-freedom (2DOF) pointing mechanisms, including the gimbal structure, the 1-RR&2-RRR spherical parallel mechanism (SPM), and the Omni-Wrist III, are increasingly applied in tracking devices, mechanical transmission, and artificial joint. Though they share the same number of degree-of-freedom at any given configuration, they will exhibit and transfer different motion characteristics, such as rotation and rolling, when moving continuously. Thanks to the concept of operation mode, these three mechanisms' distinct continuous motion characteristics can be identified and further compared through Euler parameter quaternions, Euler angles, algebraic geometry, and axodes so that the appropriate mechanism for tracking or transmission can be selected. At first, elementary operation modes are numerated based on the number of zero components in a quaternion. In order to acquire all possible operation modes, a set of constraint equations relating to each mechanism are formulated, and an algebraic geometry method is adopted to solve the constraint equations that are much too complicated. For rotation, namely, 1DOF (one-degree-of-freedom) operation mode, its continuous rotation axes are investigated. As to rolling, namely, 2DOF operation mode, allowing for the fact that the difference in 2DOF operation mode of the three mechanisms is not intuitive, axode characteristics of the three mechanisms are investigated and compared. It is found that from the above process of identification and comparison on rotation and rolling, the three mechanisms' distinctive motion characteristics can be effectively obtained.

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Figures

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Fig. 1

A flowchart of analysis for pointing mechanisms' continuous motion characteristics

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Fig. 2

Kinematic model of the gimbal-type pointing mechanism

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Fig. 3

Kinematic model of the 1-RR&2-RRR pointing manipulator

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Fig. 4

Kinematic model of the Omni–Wrist III

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Fig. 5

Structural analysis of the Omni–Wrist III: (a) limb analysis and (b) geometry analysis

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Fig. 6

Coordinate frames established in the Omni–Wrist III

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Fig. 7

Axodes when β is π/6 and α varies from 0 to 2π

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Fig. 8

Axodes when α  = 0 and β varies from 0 to π/2

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Fig. 9

Axodes when β is π/6 and α changes from 0 to 2π

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Fig. 10

Axodes when β is π/4 and α changes from 0 to 2π

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Fig. 11

Axodes when β is π/6 and α changes from 0 to 2π

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Fig. 12

Axodes when β is π/4 and α changes from 0 to 2π

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